Methods, Systems and Devices to Shape a Pressure*Time Wave Applied to a Projectile to Modulate its Acceleration and Velocity and its Launcher/Gun&#39;s Recoil and Peak Pressure Utilizing Interior Ballistic Volume Control

ABSTRACT

Methods, systems, and devices to shape a pressure*time wave applied to sniper and dangerous game rifle projectiles whereby an ammunition shell casing&#39;s volume, at release of the projectile from the casing, and rifle system impedance (Z) in conjunction with the amount of propellant are modulated to beneficially shape the wave applied to the projectile&#39;s base, and by Newton&#39;s 2 nd  law the projectile&#39;s applied acceleration*time impulse wave, to reliably reduce the velocity of a sniper or dangerous game rifle&#39;s ammunition to a sub-Mach 1 level, preserve the projectile momentum, maintain the rifle&#39;s automatic shell casing ejection and new shell casing/projectile re-load action and maintain a projectile and rifle operation within their material&#39;s strength limits. These tools are further applied to simulate severe g acceleration environments for commercial and military weapon sub-system component&#39;s non-destructive testing and certification that are carried in a projectile and applicable to any existing propellant launcher/gun system.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to the earlier filed provisionalapplication having Ser. No. 62/384,420 and hereby incorporates subjectmatter of the provisional application in its entirety.

TECHNICAL FIELD

The present specification relates to shaping an interior ballisticpressure*time wave, applied to a projectile within a projectilelauncher/gun system, by control of launcher/gun system internal volumeand thereby the launcher/gun system impedance to tailor a projectile'sresulting base applied acceleration*time wave for the purpose ofmodulating the projectile's acquired velocity and beneficiallycontrolling the projectiles applied peak acceleration, the launcher/gunsystem's internal peak pressure, preservation of the automatic spentprojectile shell casing ejection and re-loading of new projectile andshell casing and the launcher/gun recoil.

BACKGROUND

Presently fixed impedance projectile bodies, called off-springprojectiles, are imparted a specific velocity via a launcher/gun systemwith an off-spring projectile barrel/guide attached to the launcher/gunsystem. A static, internal to the launcher/gun, fixed closed propellantchamber volume, called the off-spring projectile's parent-case, isintegral to the off-spring projectile. The off-spring projectile has aspecific system impedance (Z) that is equal to the ratio of the force(F) delivered to the off-spring projectile divided by the final velocity(V_(f)) obtained by the off-spring projectile at barrel/guide exit ofthe base of the off-spring projectile:

Z=F/V _(f)

This equation is an internal launcher/gun ballistic analog to Ohm'selectrical law R=V/I; where (R) is analogous to (Z) impedance, Force (F)is analogous to Voltage (V) and Current (I) is analogous to Velocity(V_(f)). In English engineering units for the above equation F=#, thesymbol for the physical weight of an off-spring projectile and V_(f) isthe final velocity of the off-spring projectile's base at exit from thebarrel/guide. The equation reduces to the form

Z=J;

where (Z) is the modulator that amplifies or attenuates the impulse (J)wave as it accumulates per distance of off-spring projectile travel downa barrel/guide and (J) is now the impulse per unit distance in Englishengineering units of g*#*seconds per foot, where * indicatesmultiplication as a continuum running integral during off-springprojectile travel per unit distance down the barrel/guide and untiloff-spring projectile base exit, and one g is the acceleration due togravity at the Earth's surface and is the standard unitless gravitysymbol g and therefore the specific system impulse force (F) termamplitude modulator. Within the parent-case solid chemical propellantgrains are contained and then ignited by a primer, consisting of shocksensitive chemicals that are ignited either mechanically or electricallyand that expose the contained propellant grains residing within theparent-case to the fire produced by the primer to then in turn ignitethe propellant grains, and subsequently burn the propellant grainsrapidly changing the solid propellant grains into a gas in themillisecond time frame. This gas produces a pressure*time wave that isapplied in real time to the base of a parent case coupled off-springprojectile transferring the gas momentum to the off-spring projectileand by Newton 2^(nd) Law imparts an acceleration*time (g*second) impulse(J) wave per unit travel (distance) to the off-spring projectile for thepurpose of imparting a velocity (g*seconds) to the off-spring projectilethereby launching it toward a target at the acquired final velocityV_(f). Currently the parent-cases, also known as propellant chambers, ofa launcher/gun are fixed geometry devices with fixed initial volumes andintegral to a fixed barrel/guide and the off-spring projectiles have afixed system impedance that is a linear function of the off-springprojectile's weight. The barrel/guide's function is to drop theacceleration*time impulse wave on the base of the off-spring projectileby opening additional volume with the piston effect of an off-springprojectile traveling down the barrel/guide as the acceleration*time waveis applied and the impulse (J) accumulates. The system impedance (Z)controls the g amplitude applied to the off-spring projectile's base andthe time duration that the acceleration*time impulse wave is applied tothe off-spring projectile's base. System impedance (Z) control modulatesthe area underneath the acceleration*time curve modulating velocityV_(f) to newer and more beneficial levels. Present art requires newparent-cases and barrel/guides be built when the requirements ofvelocity, acceleration, recoil, and peak pressure change outside thevery narrow design space of the material strengths of the off-springprojectiles, launcher/guns, parent-cases, or barrel/guides. The presentinvention is based on the very creative verified premise that theparent-case volume is nearly constant during initial momentum transferand rise to peak pressure from the gas to the off-spring projectileproviding an inflection point that is highly sensitive to off-springprojectile geometry, mass properties and parent-case volume with whichto change peak applied pressure and system impedance (Z) and thereby theacceleration*time impulse wave (J); that is, peak pressure is applied tothe off-spring projectile before it moves significantly down thebarrel/guide and opens up additional volume. In the event off-springprojectile movement will not open significant volume during rise time towave peak pressure amplitude and this provides a sensitive inflectionpoint, where the g modulator can be applied by changing the systemimpedance or the parent-case volume during first release of theoff-spring projectile from the parent-case and therefore modulate all alauncher/gun's system parameters to more beneficial values. At thisinflection point the parent-case's volume can be modulated withoff-spring projectile mass property and geometry changes and return asignificant change in the system impedance with which to providesignificant modulation of the off-spring projectile's velocity andrecoil and/or dynamically reconfigure the parent-case to anothergeometry with a different volume in real time using a malleable formableinsert material inside the parent-case. The concepts are subtle. If oneis opening a large volume within the barrel/guide by off-springprojectile movement while the re-configuration of a parent-case geometrytakes place or adjustment of the system impedance thru off-springprojectile mass property and geometry changes, then the effect isdiminished significantly and re-shaping the pressure*time wave byadjusting the impedance or parent case volume is negated. The dynamicvolume change and adjustment of the system impedance in this invention,taking place at the unique system inflection point during a state ofnear constant volume, thereby allows a real time change to the outputpressure*time wave, which by Newton's 2^(nd) Law changes the appliedacceleration*time impulse (J) wave to the off-spring projectile and itsimpedance during transit down the barrel/guide and therefore itsimparted applied acceleration, final velocity, launcher/gun recoil, andlauncher/gun system peak pressure. This real-time change of theacceleration*time impulse wave to the off-spring projectile has thebeneficial effect of utilizing pre-existing closed volume parent-casesand barrel/guides for a much larger design space for new systemvelocity, recoil, peak pressure, and peak acceleration as thebarrel/guide exit off-spring projectile velocity in a modern daystandard launcher/gun can be tailored to a more desired level by an apriori change to the off-spring projectile's mass properties and/ordynamically changing the geometry of existing ammunition, that is, thecombination parent-case and off-spring projectile and therefore systemimpedance and the off-spring projectile's applied pressure*time waveupon ignition of the propellant and/or the modulation of the propellantmass. In this manner, existing ammunition parent-cases and expensivelauncher/guns can be used for a much wider range of velocities andacceleration requirements and other beneficial scenarios forlauncher/gun systems such as control of internal peak pressure andacceleration applied to an off-spring projectile thereby maintaining thetotal launcher/gun system and the off-spring projectile within theirmaterials' strength and system operating parameters.

In addition to changing the parent-case volume and the off-springprojectile's mass properties and/or geometry to modulate the systemimpedance during momentum transfer at the system inflection point, theoff-spring projectile can be fixed to the parent-case at the inflectionpoint to provide a back-pressure and create a virtual mass to change theoff-spring projectile's mass properties. The virtual mass method changesthe system impedance but only as a partial running continuum integral,not a full barrel length continuum running integral, as a physicalchange in mass properties of the off-spring projectile or the dynamicre-configuration of the parent-case volume will accomplish, and thevirtual mass properties method is only applied during the period thatthe off-spring projectile is releasing from the parent-case. This hasthe effect of chopping off a portion of the beginning of thepressure*time wave, reducing the area underneath the pressure*time curvethereby reducing off-spring projectile acceleration and subsequentvelocity and launcher/gun recoil. The back-pressure value can bemodulated by using different attachment techniques thereby furthermodulating the reduction of off-spring projectile velocity.

In addition to providing a larger operating space for launcher/guns andtheir existing parent-case chambers and their off-spring projectilesthis invention reduces a launcher/gun's recoil due to a reduction inoff-spring projectile final velocity V_(f). This allows smaller framedand physically vulnerable individuals the ability to operate largercaliber weapons with which to afford themselves increased personnelprotection.

Modern day sniper and dangerous game rifles equipped with optical scopessee further than the rifleman can accurately target an object. A sniperor dangerous game rifle's (launcher/gun) exit velocity is above Mach 1,which is the speed of sound or substantially 1100 feet/second dependingon the atmospheric conditions within the barrel/guide of a rifle. Thereis a range to a target where the off-spring projectile slows down andpasses, that is, backs thru Mach 1. When an off-spring projectile passesthru Mach 1 it experiences severe turbulence that cause the off-springprojectile to deviate severely from the path of aim and miss theacquired target. The present-day solution is to reduce the amount ofpropellant in the parent-case to reduce V_(f) to the sub-Mach 1 velocityregime at rifle (launcher/gun) barrel/guide exit. This has twoundesirable effects: 1) A rifle's automatic bolt action to eject thespent parent-case and reload a new parent-case with a new off-springprojectile will not work or worse is un-reliable and 2) The momentumdelivered to the target is severely reduced making the rifle unusablefor dangerous game. This invention preserves automatic bolt action andmomentum of the off-spring projectile.

Current art for testing the g tolerance for military weapon systems andvehicles and commercial vehicles is to destructively test the system.This invention will simulate a range of severe impact and vibrationenvironments by tailoring the acceleration*time impulse wave applied toan off-spring projectile inside of a launcher/gun and containing withinthe off-spring projectile the components to be evaluated to a desiredcustom acceleration*time impulse (J) wave load. This permitsnon-destructive component testing of acceleration*time impulse waveloaded subsystems such as automobiles and military weapons and thedevelopment and certification of the sub-system components. For example,an automobile's air-bag system can be tested without undergoing anactual crash event and military weapon components such as electronicfuzes, carried explosives and structures can be tested without actualdeployment of the weapon system. As another example, a military concretepenetrating projectile (off-spring projectile) weapon system will travelthru several feet of concrete after target impact. This severely g loadsthe weapon's internal components such as electronic fuzes. Present daymethods require a massive concrete structure to be built and the weaponsystem deployed against it to ascertain internal componentfunctionality. In the event the majority of the test resources are spenton concrete not the weapon system's component testing. This inventionallows all the components of the system to be tested without hugeexpenditures of capital on items that have little to do with componenttesting and evaluation other than provide a venue to simulate the genvironment. This invention allows the allotted test and certificationresources to be directed to test and certification rather than testexpedients.

Accordingly, a need exists for beneficially shaping a pressure*time waveapplied to an off-spring projectile to modulate its appliedacceleration, imparted velocity and its launcher/gun recoil and internallauncher/gun peak pressure.

SUMMARY

In the preferred embodiments, a parent-case's volume at release of theoff-spring projectile and the system impedance (Z) in conjunction withthe amount of propellant are modified to beneficially shape the outputpressure*time wave applied to an off-spring projectile's base and byNewton's 2^(nd) law an off-spring projectile's base appliedacceleration*time impulse wave for the purpose of reliably reducing theapplied velocity of a sniper or dangerous game rifle to a sub-Mach 1level at the barrel/guide exit, preserving the off-spring projectilemomentum, maintaining the rifle's automatic parent-case ejection and newparent-case/off-spring projectile re-load action, maintaining the rifleoperation within it material strength limits and applying to anoff-spring projectile containing components to be tested and certified apre-determined acceleration*time impulse wave for the purpose ofnon-destructively testing and certifying military weapon and commercialsystem components.

BRIEF DESCRIPTION OF DRAWINGS

The embodiment set forth in the drawings are illustrative and exemplaryin nature and not intended to limit the subject matter defined by theclaims. The following brief description of the illustrative embodimentscan be understood when read in conjunction with the following drawings.

FIG. 1 schematically depicts a launcher/gun system and parent-case andoff-spring projectile and the dynamic formation of a new volume withinthe parent-case chamber of a launcher/gun utilizing a formable materialinsert and dynamically hydroforming a new volume by operating thematerial in its forming region during propellant burn and rise to peakpressure within the parent-case and/or an a priori delta (Δ) change inthe mass properties of the off-spring projectile to effect a (Δ) (Z)impedance modulation and therefore a (Δ) (J) per unit distance impulsemodulation.

FIG. 2 schematically depicts on the top schematic the creation of avirtual mass and on the bottom an a priori modulation of the off-springprojectile mass properties and/or geometry to modulate system impedance(Z) and volume during dynamic propellant burn at the system inflectionpoint negating any large initial volume expansion due to thebarrel/guide piston effect and modulate the final velocity of theoff-spring projectile and the recoil of a launcher/gun system.

FIG. 3 graphically depicts on the left graph the percent appliedoff-spring projectile base pressure versus the percent of off-springprojectile base pressure wave application time and on the right graphthe percent of applied off-spring projectile base pressure versuspercent of off-spring projectile barrel/guide travel during release fromthe parent-case and rise to the peak pressure and further identifies thesystem inflection point for the launcher/gun case.

FIG. 4 graphically depicts in the percent of pressure*time waveapplication time and per cent of peak applied pressure the appliedoff-spring projectile's base pressure*time wave of a parent-case chamberbefore and after dynamic volume control by hydro-forming a new volumewithin the parent-case and before and after volume reductions due to apriori mass property or geometry changes to the off-spring projectilethereby in the case shown increasing a launcher/gun system impedance(Z).

FIG. 5 graphically depicts, in percent of full applied pressure, thepressure*time wave applied to the base of an off-spring projectile bythe formation of new off-spring projectile virtual mass properties bycreation of these new properties by the formation of a back pressure toreduce the final velocity by reducing the area under the pressure*timecurve applied to the off-spring projectile base, thereby reducing thearea under the acceleration*time curve applied to the off-springprojectile in percent of wave application time.

DETAILED DESCRIPTION OF DRAWINGS

FIG. 1 depicts the forward part of a launcher/gun system 100 showing theoff-spring projectile 140, parent case 150 and barrel/guide 180 with amalleable formable material insert 120 surrounded by air whose purposeis to dynamically create a new volume during rise to peak pressure atthe system inflection point 152, the expansion of 120 to a new 122geometry in the space previously occupied by air, the propellant grains130 within the parent-case 150, the propellant changed to a gas 132 byignition of the propellant 130 by the parent-case primer 160, theoff-spring projectile 140 with a new system impedance (ΔZ) and thebarrel/guide 180.

The malleable formable insert 120 fully captures the propellant grains130 before ignition by primer 160. Fully capturing the propellant grains130 before ignition prohibits the propellant grains 130 fromrepositioning in random patterns during handling and firing of thecombination parent-case 150/off-spring projectile 140. This preventsvariances in the barrel/guide 180 exit velocity V_(f) of the off-springprojectile 140 and maintains reliable ignition of the propellant 130from shot to shot.

The insert material 120 is selected to be formable during propellantburn, that is, the material operates within its plastic regime calledthe hydroforming regime and defined on FIG. 1 as the forming regiondotted horizontal line on the material's stress versus strain curve.During ignition of the primer 160 and burn of the solid propellant 130,changing 130 into a gas 132, the insert 122 is formed on the walls ofthe parent-case thereby dynamically increasing parent-case 150 volume atthe system inflection point 152. This volume expansion modulateslauncher/gun system parent-case 150 peak pressure, system impedance (Z),off-spring projectile velocity V_(f), launcher/gun recoil and appliedbase off-spring projectile 140 applied pressure and acceleration.

FIG. 2 top depicts the creation of a virtual mass constituting a backpressure or null force to dynamically change the mass properties of theoff-spring projectile 140 during release of the off-spring projectile140 from the parent-case 150 at the inflection point 152. The off-springprojectile 140, normally crimped to a parent-case with only a minimalresisting back pressure force, is in order of joint 170 shear strengthresistances from high to low; brazed, soldered, glued or threaded to theparent-case for the purpose of providing a resistance to movement andkeeping the volume of the parent-case 150 constant until joint 170'sshear resistance strength is overcome; and then permitting movement downthe barrel/guide 180 of the off-spring projectile. This has the effectof nulling that portion of the pressure*time curve until the pressurerises to a value that it overcomes the shear strength of the joint 170and the off-spring projectile 140 begins movement down the barrel/guide180 and opens additional volume. FIG. 2 bottom shows the option of a (Δ)mass property modulation of off-spring projectile 140 linearly producinga (ΔZ) system impedance thereby reducing or increasing the percentage ofbarrel/guide 180 travel during rise to peak pressure thereby reducing orincreasing the parent-case 150 volume at the inflection point 152 duringrelease of the off-spring projectile 140 from the parent-case andthereby modulating system impedance (Z).

The FIG. 3 left graph is the normalized to 100% peak pressure of thepressure*time wave versus normalized to 100% percent of pressure*timewave application time of a common fixed volume and fixed systemimpedance parent-case 150 pressure chamber with no new volume formeddynamically by a formable material insert 120 or adjustments to theoff-spring projectile 140 mass properties either virtually orphysically. The right graph is the normalized to 100% off-springprojectile 140 peak pressure obtained versus normalized to 100%barrel/guide 180 off-spring projectile 140 base travel for this commoncase. In the event the off-spring projectile 140 piston effect ofopening a new volume is substantially 6% of the off-spring projectile140 travel as the volume remains near constant during momentum transferfrom propellant gas 132 to off-spring projectile 140 and reachingmaximum pressure at the inflection point 152 within the parent-case 150.This graph identifies the common case system inflection point 152 as afunction of barrel/guide 180 off-spring projectile 140 travel at 100%peak applied base off-spring projectile 140 pressure.

FIG. 4 depicts the results of the real-time modulation of theparent-case 150 volume and/or an a priori physical change to the massproperties and/or geometry of the off-spring projectile 140 innormalized percent of parent-case peak pressure applied to theoff-spring projectile 140 versus percent of time the pressure*time waveis applied to the off-spring projectile 140 and thereby a modulation ofthe system impedance (Z). The solid line is the pressure*time wave curveapplied to the off-spring projectile 140 without dynamic volumeexpansion within the parent-case 150 or change in off-spring projectile140 mass properties; the dotted line shows the pressure*time results dueto system impedance (Z) modulation by dynamic hydroforming of a newvolume within the parent-case 150 or dynamic forming of a new volume byinhibiting off-spring projectile 140 movement during release from theparent case 150 due to changes to the off spring projectile 140 massproperties or geometry. These graphs reflect a change to a higher valueof system impedance (Z). The graphs would be reversed for a lower valueof system impedance (Z),

FIG. 5 depicts normalized percentage results for an 80 percent pressurelevel that overcomes the shear strength of joint 170. The hatched areaon the left graph is the area that is lost as a result of the backpressure formed by the joint 170 which nulls a portion of theacceleration*time wave area application to the off-spring projectile140. The graph to the right is the resulting pressure*time wave appliedto the off-spring projectile 140 that modulates velocity and recoil inthis illustration to a higher value of system impedance (Z) due to theformation of a virtual mass, that is, back pressure.

What is claimed is:
 1. A pressure*time wave, where the symbol *indicates a running continuum integral as an off-spring projectiletraverses the barrel/guide of a rifle, re-shaping method to reliablyobtain a sub-Mach 1 rifle barrel/guide exit velocity and preserveautomatic operation of standard automatic rifles (launcher/guns) used assniper rifles and dangerous game rifles and for stabilization of theoff-spring projectile's transit to a sniper's target or dangerous gametarget thereby maintaining the rifle operator's aim point, where Mach 1is the speed of sound in the atmosphere within the confines of a rifle'sbarrel/guide, or substantially 1100 feet/second, in which an off-springprojectile is launched by internal volume control and further applied tothe base of a sniper or dangerous game rifle's off-spring projectilewhereby the off-spring projectile is attached to an accompanyingparent-case containing solid propellant grains by modifying the riflesystem's internal volume at initial propellant ignition and thereby itsimpedance Z=F/V_(f)=J where (Z) is the rifle system's impedance in theEnglish engineering units of g*#*seconds/foot and J in equal units isthe per unit distance impulse delivered to an off-spring projectile, andfurther one g is the unitless acceleration due to gravity at the Earth'ssurface and is the standard unitless gravity symbol g, # is the symbolfor the physical weight of an off-spring projectile, F is the deliveredforce in units of g*# to the base of the off-spring projectile and V_(f)is the final velocity of the off-spring projectile at the riflebarrel/guide's exit in g*seconds and further applied at the riflesystem's inflection point located at the attainment of the riflesystem's peak pressure occurring at the end of the time consumed byinitial momentum transfer from the parent-case propellant ignition gasesto off-spring projectile's base and during first release of theoff-spring projectile from an attached off-spring projectile'sparent-case and rise to peak pressure and peak g acceleration on theoff-spring projectile's base after ignition of the rifle's propellantgrains and further during the initial movement of the off-springprojectile resulting in a change in the parent-case volume, tobeneficially modify the off-spring projectile's final velocity V_(f) atrifle barrel/guide exit and applied peak acceleration of a rifle systemand peak internal pressure of the rifle system, and preservingsufficient momentum to operate the rifle's automatic ejection of theoff-spring projectile's spent parent-case and reloading of a newcombination parent-case and off-spring projectile, said methodcomprising the steps of: Increasing the material density of theoff-spring projectile thereby increasing its mass properties andlowering the system impedance (Z) to provide resistance to movement atthe rifle system's inflection point thereby reducing the initialparent-case volume and occurring at first release of the off-springprojectile from the parent-case and at the system inflection pointlocated at the first release point of the off-spring projectile from itsparent-case; Reducing the amount of propellant grains in the parent-caseby an amount that will preserve off-spring projectile momentum therebysatisfying the momentum equation M_(N)×V_(FN)=M_(O)×V_(FO), where xindicates multiplication, thereby keeping the rifle's operatingconditions within the limits of the rifle's material properties andretaining proper ejection of the parent-case and re-loading of anew-parent-case with off-spring projectile and where M_(N) is the newvalue of the off-spring projectile mass, V_(FN) is the desired new finalvelocity V_(f) of the off-spring projectile at the off-springprojectile's base rifle barrel/guide exit, M_(O) is the former value ofthe off-spring projectile mass and V_(FO) is the former value of thevelocity V_(f) of the off-spring projectile at off-spring projectilebase rifle barrel/guide exit.
 2. A method of claim 1 for simulatingsevere g acceleration environments for commercial or military weaponsub-system component's non-destructive testing and certification andapplicable to the full suite of existing propellant launcher/guns andmaintaining the launcher/gun system operation within the launcher/gun'smaterial property limits and operating parameters by volume andoff-spring projectile mass properties control and thereby systemimpedance (Z) control within any launcher/gun system to tailor thepressure*time wave and therefore the per distance unit impulse (J) inthe equation Z=F/V_(f)=J applied to an off-spring projectile containingcomponents to be tested and certified and the resulting gacceleration*time impulse wave to the desired value for application tomilitary or commercial components during launch from a launcher/gunsystem containing an off-spring projectile with the components to betested or certified therein for the purposes of testing the g toleranceof the components and/or certification of the components, said methodscomprising the steps of: Defining the required g amplitude and militaryor commercial component exposure time in seconds to be applied to thecomponents to be tested and dividing this value of g*time, where thesymbol * indicates a continuum running integral as an off springprojectile traverses the barrel/guide, by the length of the barrel/guidethereby forming the value of the system impedance (Z) required for theequation Z=F/V_(f)=J, where (Z)=(J) is the system impedance and perdistance unit impulse respectively in English engineering units ofg*#*seconds/foot, g*# is the delivered force (F) to an off-springprojectile and # is the symbol for the physical weight of a bullet inpounds, V_(f) is the final velocity of an off-spring projectile at thelauncher/gun barrel/guide's exit in feet/second and one g is theacceleration due to gravity at the Earth's surface and is the standardunitless gravity symbol g: Modifying the off-spring projectile massthereby the off-spring projectile's mass properties and parent caseinitial volume and final velocity V_(f) at off-spring projectile basebarrel/guide exit to obtain the desired characteristic impedance (Z) inthe equation Z=F/V_(f)=J and reducing the amount of propellant in thelauncher/gun system by an amount that will preserve off-springprojectile momentum that will satisfy the momentum equationM_(N)×V_(FN)=M_(O)×V_(FO) to retain the gun's operating conditionswithin the limits of the gun's material properties, where M_(N) andV_(FN) are the new values of the off-spring projectile mass and finalvelocity of the off-spring projectile at off-spring projectile basebarrel/guide exit that yield the desired system impedance (Z) and M_(O)and V_(FO) are the former values of an off-spring projectile's mass andvelocity at off-spring projectile base barrel/guide exit that wereunequivocally demonstrated to maintain the gun's operating conditionswithin the limits of the gun's material properties and operatingparameters.